Finite Group Databasebeta

← #29663414

Subgroups — #29663414

Order 15616.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457157C212yesmaximal
2#21456405C211yesmaximal, characteristic, complemented
3#21454794C211yesmaximal, characteristic
4#21445374C212yesmaximal, complemented
5#21445367C212yesmaximal, complemented
6#21445214C211yesmaximal, characteristic, complemented
7#21445209C211yesmaximal, characteristic, complemented
8#21445190C211yesmaximal, characteristic, complemented
9#21445185C211yesmaximal, characteristic, complemented
10#21444517C212yesmaximal, complemented
11C2×C61×#335C211yesmaximal, characteristic, complemented
12#16840319C2212yes—
13#16840296C2211yescharacteristic
14#16840167C2211yescharacteristic
15#16840142C2211yescharacteristic
16#16840113C2212yes—
17#16840070—22no—
18#16840048C2212yes—
19#16840043C2212yes—
20#16840003—22no—
21#16840003—21no—
22#16840003—21no—
23#16839991—22no—
24#16839985—22no—
25#16839973C2212yes—
26#16839968C2212yes—
27#16839892C2211yescharacteristic
28C8×Dic122C2211yescharacteristic
29C4×Dic244—21no—
30C4×Dic244—21no—
31#16839841C2211yescharacteristic
32#16839833—21no—
33C8×D244C2211yescharacteristic
34C8×C22⋊D61—21no—
35#16839821—21no—
36#16839819C2211yescharacteristic
37#16839716—21no—
38#16839509C2212yes—
39#16839509C2212yes—
40#16839507C2212yes—
41#16839507C2212yes—
42C2×C4⋊C8×C61C2212yes—
43C2×C4×C8×C61C2211yescharacteristic
44C61×#335C2211yescharacteristic
45C61×#335C2211yescharacteristic
46C61×#335C2212yes—
47C2×Dic244—21no—
48C2×Dic244—21no—
49C2×Dic244—22no—
50C2×#11758190—22no—
51C2×#11758189—21no—
52C2×C8×D61—21no—
53#14519777C2312yes—
54#14519777C2312yes—
55#14519771—21no—
56#14519769—22no—
57#14519769D411yescharacteristic
58#14519765D411yescharacteristic
59#14519760—21no—
60#14519756—22no—
61#14519756—22no—
62#14519756D411yescharacteristic
63#14519751D411yescharacteristic
64C4×Dic122—22no—
65C4×Dic122—22no—
66C4×Dic122C2311yescharacteristic
67C4×D244C2311yescharacteristic
68C4×C22⋊D61—21no—
69#14519736—22no—
70#14519734—21no—
71#14519711—21no—
72#14519711—21no—
73#14519711—22no—
74#14519709—22no—
75C4⋊#92418C2311yescharacteristic
76C4⋊#92418C2311yescharacteristic
77#14519706—21no—
78#14519706—21no—
79#14519702—22no—
80#14519702—22no—
81#14519702—22no—
82#14519702—22no—
83#14519702—22no—
84#14519699—22no—
85C22⋊#92418—21no—
86#14519689—21no—
87#14519689—21no—
88#14519688—21no—
89#14519687—21no—
90C8×Dic61—21no—
91C22×C8×C61—22no—
92C22×C8×C61D411yescharacteristic
93C22×C8×C61D411yescharacteristic
94C2×C42×C61C2311yescharacteristic
95C4⋊C8×C61—22no—
96C4⋊C8×C61C2312yes—
97C4⋊C8×C61C2312yes—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C2×C22⋊D61—21no—
106C2×D244C2×D411yescharacteristic
107C2×C4×D61—21no—
108C2×Dic122—22no—
109C2×Dic122—22no—
110C2×Dic122C2×D411yescharacteristic
111C2×C8×C61—22no—
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—41no—
115C2×C8×C61—82no—
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123C42×C61C2411yescharacteristic
124C22⋊Dic61—21no—
125C22⋊Dic61—42no—
126#11758198—21no—
127#11758198—21no—
128#11758198—21no—
129#11758198—21no—
130C4⋊Dic61—22no—
131C4⋊Dic61—22no—
132C4⋊Dic61—22no—
133C4⋊Dic61—22no—
134C4⋊Dic61C2×D411yescharacteristic
135C4⋊Dic61C2×D411yescharacteristic
136#11758196—21no—
137#11758196—21no—
138#11758196—21no—
139#11758196—21no—
140#11758196—42no—
141#11758196—42no—
142C4×Dic61—21no—
143C4×Dic61—42no—
144C2×#92418—21no—
145C2×#92418—21no—
146Dic244—42no—
147Dic244—42no—
148Dic244—82no—
149#11758190—82no—
150#11758189—42no—
151C8×D61—42no—
152C23×C61#12111yescharacteristic
153C22×D61—21no—
154C2×C4×C61—22no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61C22×D411yescharacteristic
163C2×C4×C61C22×D411yescharacteristic
164C2×C4×C61C2×#4111yescharacteristic
165C22⋊D61—42no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171D244—21no—
172D244—21no—
173C4×D61—41no—
174C4×D61—41no—
175Dic122—21no—
176Dic122—21no—
177Dic122—42no—
178Dic122—42no—
179Dic122—42no—
180Dic122—42no—
181C8×C61—21no—
182C8×C61—21no—
183C8×C61—21no—
184C8×C61—42no—
185C8×C61—42no—
186C8×C61#13512yes—
187#92418—41no—
188#92418—41no—
189#19223—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61#47312yes—
193C22×C61C2×#12111yescharacteristic
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61C2×#13511yescharacteristic
202C4×C61#57511yescharacteristic
203C4×C61#57611yescharacteristic
204C4×C61#57811yescharacteristic
205Dic61—41no—
206Dic61—41no—
207Dic61—41no—
208Dic61—82no—
209Dic61—82no—
210#3248—612no—
211#3170—611no—
212#2966—611no—
213#1700—612no—
214#1699—612no—
215#1674—611no—
216#1673—611no—
217#1670—611no—
218#1669—611no—
219C2×#335D6111yescharacteristic, complemented
220#1552—612no—
221C2×C61—22no—
222C2×C61#303511yescharacteristic
223C2×C61#306111yescharacteristic
224C2×C61C2×#47311yescharacteristic
225D61—81no—
226#533—612no—
227#529—611no—
228#500—611no—
229#494—611no—
230#487—612no—
231#479—1222no—
232#475—612no—
233#474—612no—
234#467—1222no—
235#467—1221no—
236#467—1221no—
237#465—1222no—
238#464—1222no—
239#462—612no—
240#461—612no—
241#446—611no—
242C8×Q8—611no—
243C4×Q16—1221no—
244C4×Q16—1221no—
245#436—611no—
246#435—1221no—
247C8×D4—611no—
248C8×D4—1221no—
249#433—1221no—
250#432—611no—
251C2×C4⋊C8C2×D6112yes—
252#405—1221no—
253C2×C4×C8C2×D6111yescharacteristic
254#335C2×D6111yescharacteristic
255#335C2×D6111yescharacteristic
256#335C2×D6112yes—
257#332—612no—
258#332—612no—
259#332—612no—
260#332—612no—
261C61#1922311yescharacteristic, complemented, Sylow
262C2×Q16—1222no—
263C2×Q16—1221no—
264C2×Q16—1221no—
265C2×SD16—1222no—
266C2×M16—1221no—
267C22×C8—22no—
268C22×C8—1221no—
269C22×C8D24411yescharacteristic
270C22×C8D24411yescharacteristic
271C4⋊Q8—612no—
272C4⋊Q8—612no—
273#126—1221no—
274#125—611no—
275#125—1222no—
276#124—611no—
277#123—1221no—
278C22⋊Q8—611no—
279C22⋊Q8—1222no—
280C22⋊Q8—1222no—
281#121—611no—
282C4×Q8—611no—
283C4×Q8—1222no—
284C4×Q8—1222no—
285C4×D4—611no—
286C4×D4—1221no—
287#117—1221no—
288#117—1222no—
289C2×C42C22×D6111yescharacteristic
290#107—1222no—
291#107—1221no—
292#107—1221no—
293#106—1222no—
294C4⋊C8—22no—
295C4⋊C8—611no—
296C4⋊C8—611no—
297C4⋊C8—1221no—
298C4⋊C8—1221no—
299C4⋊C8C22×D6112yes—
300C4⋊C8C22×D6112yes—
301#103—1222no—
302#103—1222no—
303#103—1222no—
304#103—1222no—
305#103—1222no—
306#102—1222no—
307C22⋊C8—1221no—
308C22⋊C8—1221no—
309C22⋊C8—1221no—
310#97—1221no—
311#97—1221no—
312C4×C8—1221no—
313C4×C8D24411yescharacteristic
314C4×C8D24411yescharacteristic
315C4×C8C22×D6111yescharacteristic
316C4×C8C22×D6111yescharacteristic
317C2×Q8—611no—
318C2×Q8—1222no—
319C2×Q8—1222no—
320C2×D4—611no—
321C2×D4—1221no—
322C22×C4—1221no—
323C22×C4C2×D24411yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4#1175822611yescharacteristic
326Q16—4882no—
327Q16—2442no—
328Q16—2442no—
329SD16—4882no—
330M16—2442no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—82no—
336C2×C8—1221no—
337C2×C8—1221no—
338C2×C8—2442no—
339C2×C8C2×D24411yescharacteristic
340C2×C8C2×D24411yescharacteristic
341C2×C8C2×D24411yescharacteristic
342C2×C8C2×D24411yescharacteristic
343C4⋊C4—611no—
344C4⋊C4—611no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—1222no—
350C4⋊C4—1222no—
351C4⋊C4—1222no—
352C4⋊C4—1222no—
353C4⋊C4—2442no—
354C4⋊C4—2442no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C22⋊C4—2442no—
361C42—1221no—
362C42—2442no—
363C42C2×D24411yescharacteristic
364C42D4×D6111yescharacteristic
365C42#1175822611yescharacteristic
366C42C23×D6111yescharacteristic
367C23—1221no—
368C23#1451975211yescharacteristic
369Q8—1221no—
370Q8—1221no—
371Q8—2442no—
372Q8—2442no—
373Q8—2442no—
374Q8—2442no—
375D4—1221no—
376D4—1221no—
377D4—2442no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4#1451975211yescharacteristic
391C2×C4#1451975211yescharacteristic
392C2×C4#1451975211yescharacteristic
393C2×C4C2×D4×D6111yescharacteristic
394C2×C4C22×D24411yescharacteristic
395C2×C4C2×#1175822611yescharacteristic
396C8—21no—
397C8—21no—
398C8—21no—
399C8—42no—
400C8—42no—
401C8—2441no—
402C8—2441no—
403C8#1451979912yes—
404C22—21no—
405C22—21no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22#1684003812yes—
410C22C2×#1451975211yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—4882no—
416C4—4882no—
417C4—2441no—
418C4—2441no—
419C4—2441no—
420C4C2×#1451979911yescharacteristic
421C4#1684056211yescharacteristic
422C4#1684056311yescharacteristic
423C4#1684057511yescharacteristic
424C2—22no—
425C2—4881no—
426C2#2145527611yescharacteristic
427C2#2145549111yescharacteristic
428C2C2×#1684003811yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#335C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenterC2×#335D61
hypocenterC61#19223
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21456405C2semidirect
4. #21445374C2semidirect
5. #21445367C2semidirect
6. #21445214C2semidirect
7. #21445209C2semidirect
8. #21445190C2semidirect
9. #21445185C2semidirect
10. #21444517C2semidirect
11. C2×C61×#335C2semidirect
219. C2×#335D61semidirect
261. C61#19223semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214571572
#214564052
#214547942
#214453742
#214453672
#214452142
#214452092
#214451902
#214451852
#214445172
C2×C61×#3352
#1922361